cp's OEIS Frontend

A353357 Numbers k for which A353328(k) < A353329(k). Positions of -1's in A353354.

%I A353357 #16 Mar 22 2025 19:02:22
%S A353357 3,7,13,19,21,24,29,37,39,42,43,53,56,57,61,71,78,79,81,87,89,91,101,
%T A353357 104,105,107,111,113,114,129,131,133,139,151,152,159,163,168,173,174,
%U A353357 181,182,183,189,192,193,195,199,203,213,222,223,229,231,232,237,239,247,251,258,259,263,266,267,271,281,285,293
%N A353357 Numbers k for which A353328(k) < A353329(k). Positions of -1's in A353354.
%C A353357 For any term k present here, A003961(k) is present in A353356.
%F A353357 {a(n) : n >= 1} = {m : tau(m) * A048675(m) == 1 (mod 3)}, where tau is the number of divisors function, A000005.
%o A353357 (PARI)
%o A353357 A332823(n) = { my(f = factor(n),u=(sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2)%3); if(2==u,-1,u); };
%o A353357 A353354(n) = sumdiv(n,d,A332823(d));
%o A353357 isA353357(n) = (0>A353354(n));
%o A353357 (PARI)
%o A353357 A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
%o A353357 isA353357(n) = (1==((numdiv(n)*A048675(n))%3));
%Y A353357 Cf. A000005, A003961, A048675, A332823, A353328, A353329, A353354, A353355, A353356.
%K A353357 nonn
%O A353357 1,1
%A A353357 _Antti Karttunen_ and _Peter Munn_, Apr 15 2022